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SageMath
E = EllipticCurve("dq1")
E.isogeny_class()
Elliptic curves in class 76050.dq
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 76050.dq1 | 76050ge2 | \([1, -1, 1, -13838090, 18260541537]\) | \(666276475992821/58199166792\) | \(25598494380593548089000\) | \([2]\) | \(8257536\) | \(3.0403\) | |
| 76050.dq2 | 76050ge1 | \([1, -1, 1, -13533890, 19167057537]\) | \(623295446073461/5458752\) | \(2400993692855784000\) | \([2]\) | \(4128768\) | \(2.6937\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 76050.dq have rank \(0\).
Complex multiplication
The elliptic curves in class 76050.dq do not have complex multiplication.Modular form 76050.2.a.dq
sage: E.q_eigenform(10)
Isogeny matrix
sage: E.isogeny_class().matrix()
The \(i,j\) entry is the smallest degree of a cyclic isogeny between the \(i\)-th and \(j\)-th curve in the isogeny class, in the LMFDB numbering.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
